1. Field of the Invention
The present invention relates to computer data processing and graphics.
2. Related Art
Many current multi-channel graphics cards (hereafter referred to as "limited-precision" graphics cards or hardware) cannot resample and accumulate high-precision data. Precision is limited in multi-channel graphics cards for two main reasons. First, texture mapping hardware may not support interpolation of data greater than a precision bit threshold, e.g. twelve bits. Second, an accumulation buffer may not be available. For example, an Impact.TM. computer made by Silicon Graphics, Inc. has a limited-precision graphics card. The Impact.TM. computer supports up to four 12-bit channels of texture data in texture random access memory (12/12/12/12 for 4 TRAM and 4/4/4/4 or 8/8 for 1 TRAM). The frame buffer can be configured to hold eight-bit red, green, blue, and alpha texture channels (RGBA 8/8/8/8) or 12-bit red, green, and blue texture channels (RGB 12/12/12). Impact.TM. graphics hardware generally has no hardware accumulation buffer.
Precision limitations in graphics hardware are especially constraining in medical applications, such as, computer tomography (CT). For example, Cabral et al. recently introduced thc use of hardware texture mapping for fast back-projection. See, B. Cabral, N. Cam and J. Foran, "Accelerated Volume Rendering and Tomographic Reconstruction Using Texture Mapping Hardware," Proceedings of ACM/IEEE Symposium on Volume Visualization (IEEE CS Press), pp.91-98, 1994 (Order No. PR07067, 1995) (incorporated in its entirety herein by reference); and the co-pending, commonly-owned U.S. patent application by B. Cabral and J. Foran, "A System and Method of Performing Tomographic Reconstruction and Volume Rendering Using Texture Mapping," filed Jul. 7, 1995, application Ser. No. 08/499,614 (SGI Ref. No. 15-4-148.00, SKGF Ref. No. 1452.0420000) (incorporated in its entirety herein by reference).
A back-projection algorithm is used to reconstruct a CT image out of its projected sinograms. Each pixel in a final reconstructed CT image is reconstructed as the sum of contributions of all sinogram images. The value of each pixel is a sum over all sinograms. Medical CT data is often provided in a 16 bit LUMINANCE channel.
According to the Cabral and Foran fast back-projection technique, for each pixel and sinogram, an appropriate projection point is found. The distance from the appropriate projection point to its neighboring lattice points (x and 1-x) is calculated. Linear interpolation is then used to determine a value at non-lattice point on the sinogram. Finally, the interpolated values are accumulated. In a sense, a sinogram is "smeared" over the screen and accumulated using an accumulation buffer or blending.
The Cabral and Foran technique demonstrates that the speed of back-projection (without filtering) for an N.times.N image and M sinograms of arbitrary length is proportional to N.times.N.times.M/(Texture-fill-rate). For example, performing the algorithm for a 512.times.512 image with 512 sinograms on the high-precision Reality-Engine2.TM. whose texture fill rate is 80 Mpixels/sec will take theoretically 1.6 sec. Thus, this method is very promising as fast texture mapping capabilities have migrated to desk-top computers. However, even as texture mapping speed increases, desktop computers are often limited-precision machines employing limited-precision graphics cards or hardware as described above. The texture mapping capability of a desktop computer and any other limited-precision graphics computer is thus limited and cannot support a high-precision algorithm such as the Cabral and Foran fast back-projection technique.
Precision limits of a graphics card or hardware need to be overcome. A method, system, and computer program product is needed that allows calculations requiring high-bit precision to be run on limited-precision graphics cards or hardware. High-precision data, such as 16-bit luminance data used in computer tomography, needs to be resampled and accumulated by limited-precision graphics hardware and machines. Fast back-projection as in the Cabral and Foran technique for CT reconstruction and volume rendering needs to be supported by a limited-precision graphics hardware or card, including a desktop computer.